"optislang inside ANSYS Workbench"

Transcription

1 "optislang inside ANSYS Workbench" - efficient, easy, and safe to use Robust Design Optimization (RDO) - second: part: Design Robustness and Design Reliability Johannes Will, CEO Dynardo GmbH 1

2 Agenda Introduction to Robust Design Optimization Robustness analysis Reliability Analysis Robust Design Optimization Life demonstration 2

3 Founded: 2001 (Will, Bucher, CADFEM International) More than 35 employees, offices at Weimar and Vienna Leading technology companies Daimler, Bosch, Eon, Nokia, Siemens, BMW, are supported by us Software Development Dynardo is your engineering specialist for CAE-based sensitivity analysis, optimization, robustness evaluation and robust design optimization. CAE-Consulting Our expertise: Mechanical engineering Civil engineering & Geomechanics Automotive industry Consumer goods industry Power generation 3

4 Premium Consultancy and Software Company for CAE-based Robustness Evaluation, Reliability Analysis and Robust Design Optimization using Stochastic Analysis Dynardo is the consulting company which successfully introduced stochastic analysis into complex CAE-based virtual product development processes. Recently, it is applied in the power generation industry, automotive industry and high-level consumer goods industry DYNARDO Field of Excellence 4

5 Challenges in Virtual Prototyping Virtual prototyping is necessary for cost efficiency Test cycles are reduced and placed late in the product development CAE-based optimization and CAE-based robustness evaluation becomes more and more important in virtual prototyping Optimization is introduced into virtual prototyping Robustness evaluation is the key methodology for safe, reliable and robust products The combination of optimizations and robustness evaluation will lead to robust design optimization strategies 5

6 Design for Six Sigma Six Sigma is a concept to optimize the manufacturing processes such that automatically parts conforming to six sigma quality are produced Design for Six Sigma is a concept to optimize the design such that the parts conform to six sigma quality, i.e. quality and reliability are explicit optimization goals Because not only 6 Sigma values have to be used as measurement for a robust design, we use the more general classification Robust Design Optimization 6

7 Start Robust Design Optimization Robust Design Variance based Robustness Evaluation Probability based Robustness Evaluation, (Reliability analysis) Optimization Sensitivity Study Single & Multi objective (Pareto) optimization CAE process (FEM, CFD, MBD, Excel, Matlab, etc.) 7

8 Example: Analytical nonlinear function Additive linear and nonlinear terms and one coupling term Contribution to the output variance (reference values): X 1 : 18.0%, X 2 : 30.6%, X 3 : 64.3%, X 4 : 0.7%, X 5 : 0.2% 8

9 Robustness Design Optimization 9

10 Robust Design Optimization Robust Design Optimization (RDO) optimize the design performance with consideration of scatter of design (optimization) variables as well as other tolerances or uncertainties. As a consequence of uncertainties the location of the optima as well as the contour lines of constraints scatters. To measure Design Robustness stochastic analysis become necessary. 10

11 When and How to apply RDO? When material, geometry, process or environmental scatter is significantly affecting the performance of important response values When significant scatter of performance is seen in reality and there is doubt that safety distances may be to small or safety distances should be minimized for economical reasons than stochastic analysis needs to be implemented. Iterative RDO strategies using optimization steps with safety margins in the design space and checks of robustness in the space of scattering variables or Automatic RDO strategies estimating variance based or probability based measurements of variation for every candidate in the optimization space are possible RDO strategies. 11

12 Which Robustness measurements? Robustness in terms of constraints Taguchi = Robustness in terms of the objective Safety margin (sigma level) of one or more responses y: Reliability (failure probability) with respect to given limit state: Performance (objective) of robust optimum is less sensitive to input uncertainties Minimization of statistical evaluation of objective function f (e.g. minimize mean and/or standard deviation): 12

13 What is necessary for successful implementation? 1. Introduction of realistic scatter definitions Distribution function Correlations Random fields 2. Using of reliable stochastic methodology Variance-based robustness evaluation using optimized LHS 3. Development of reliable robustness measurements Standardized post processing Significance filter Measurements of forecast quality Reliable variation and correlation measurements 13

14 Definition of Uncertainties 14

15 Uncertainties and Tolerances Design variables Material, geometry, loads, constrains, Manufacturing Operating processes (misuse) Resulting from Deterioration Property SD/Mean % Metallic materiales, yield 15 Carbon fiber rupture 17 Metallic shells, buckling strength 14 Bond insert, axial load 12 Honeycomb, tension 16 Honeycomb, shear, compression 10 Honeycomb, face wrinkling 8 Launch vehicle, thrust 5 Transient loads 50 Thermal loads 7.5 Deployment shock 10 Acoustic loads 40 Vibration loads 20 Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace. Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris

16 Definition of Uncertainties 1) Translate know how about uncertainties into proper scatter definition Yield stress Distribution functions define variable scatter Tensile strength Correlation of single uncertain values Correlation is an important characteristic of stochastic variables. Spatial Correlation = random fields 16

17 Optimal translation of scattering variables - measurement of scattering variables can be easily imported and optimal statistic translation (distribution function and correlation) can be fitted using Excel and optislang 17

18 Random Field Parametric Introduction of scatter of spatially correlated scatters need parametric of scatter shapes using random field theory. The correlation function represents the measure of waviness of random fields. The infinite correlation length reduced the random field to a simple random variable. Usually, there exist multiple scatter shapes representing different scatter sources. 18

19 Implementation of Random Field Parametric Introduction of spatial correlated scatter to CAE-Parameter (geometry, thickness, plastic values) 3. Generation of multiple imperfect structures using Random Field parametric 4. Running Robustness Evaluation including Random Field effects 2. Generation of scatter shapes using Random field parametric, quantify scatter shape importance 1. Input: multiple process simulation or measurements 19

20 Variance-based Robustness Analysis 20

21 Robustness = Sensitivity of Uncertainties 21

22 Robustness check of optimized designs With the availability of parametric modeling environments like ANSYS workbench an robustness check becomes very easy! Menck see hammer for oil and gas exploration (up to 400m deep) Robustness evaluation against tolerances, material scatter and working and environmental conditions 60 scattering parameter Design Evaluations: 100 Process chain: ProE-ANSYS workbench- optislang 22

23 Robustness Evaluation of NVH Performance Start in 2002, since 2003 used for Production Level How does body and suspension system scatter influence the NVH performance? Consideration of scatter of body in white, suspension system Prognosis of response value scatter Identify correlations due to the input scatter Up-to-date robustness evaluation of body in white have scattering variables Using filter technology to optimize the number of samples by courtesy of Will, J.; Möller, J-St.; Bauer, E.: Robustness evaluations of the NVH comfort using full vehicle models by means of stochastic analysis, VDI-Berichte Nr.1846, 2004, S , 23

24 RDO procedure of consumer goods Goal: Check and improve Robustness of a mobile phone against drop test conditions! Using sensitivity analysis the worst case drop test position as well as optimization potential out of 51 design variables was identified Robustness evaluation against production tolerances and material scatter (209 scattering parameter) shows need for improvements Safety margins are calculated with Robustness evaluation after design improvements Design Evaluations: Sensitivity 100, Robustness 150 CoD lin adj ANGLE_X = 3 CoD quad adj CoD lin adj Spearman CoP Sensi2 by courtesy of Ptchelintsev, A.; Grewolls, G.; Will, J.; Theman, M.: Applying Sensitivity Analysis and Robustness Evaluation in Virtual Prototyping on Product Level using optislang; Proceeding SIMULIA Customer Conference 2010, 24

25 Robustness evaluation as early as possible Goal: Tolerance check before any hardware exist! Classical tolerance analysis tend to be very conservative Robustness evaluation against production tolerances and material scatter (43 scattering parameter) shows: - Press fit scatter is o.k. - only single tolerances are important (high cost saving potentials) Production shows good agreement! by courtesy of Design Evaluations: 150 solver: ANSYS/optiSLang Suchanek, J.; Will, J.: Stochastik analysis as a method to evaluate the robustness of light truck wheel pack; Proceedings WOSD 6.0, 2009, Weimar, Germany, 25

26 Robustness Evaluation Minimum required user input: definition of input variation /scatter definition of robustness criteria number of samples for ALHS 26

27 Reliability Analysis 27

28 Reliability Analysis Robustness can verify relatively high probabilities only (±2σ, like 1% of failure) Reliability analysis verify rare event probabilities ( 3σ, smaller then 1 out of 1000) There is no one magic algorithm to estimate probabilities with minimal sample size. It is recommended to use two different algorithms to verify rare event probabilities First order reliability method (FORM), 2σ, gradient based Importance sampling using design point (ISPUD), Sigma level 2, n 50 Monte-Carlo-Simulation, independent of n, but very high effort for 2σ Latin Hypercube sampling, independent of n, still very high effort for 2..3σ Asymptotic Sampling, 2σ, n 10 Adaptive importance sampling, 2σ, n 10 Directional sampling, 2σ, n 10 Directional Sampling using global adaptive response surface method, 2σ, n

29 Reliability Analysis Algorithms Gradient-based algorithms = First Order Reliability algorithm (FORM) ISPUD Importance Sampling using Design Point Adaptive Response Surface Method Monte Carlo Sampling X2 Latin Hypercube Sampling Directional Sampling X1 29

30 How choosing the right algorithm? Robustness Analysis provide the knowledge to choose the appropriate algorithm Robustness & Reliability Algorithms 30

31 Application Example ARSM for Reliability Fatigue life analysis of Pinion shaft Random variables Surface roughness Boundary residual stress Prestress of the shaft nut Target: calculate the probability of failure Probability of Failure: Prestress I: P(f)= (230 ppm) Prestress II: P(f)= (0.13 ppm) sigma = +/-5kN sigma = +/-10kN Solver: Permas Method: ARSM 75 Solver evaluations by courtesy of 31

32 Robust Design Optimization 32

33 Robust Design Optimization Adaptive Response Surface Evolutionary Algorithm Pareto Optimization 33

34 Iterative RDO Application Connector 2) The DX Six Sigma design was checked in the space of 36 scattering variables using optislang Robustness evaluation. Some Criteria show high failure probabilities! 1) From the 31 optimization parameter the most effective one are selected with optislang Sensitivity analysis. 3) From optislang Robustness Evaluation safety margins are derived. 4) Three steps of optimization using optislang ARSM and EA optimizer improve the design to an optislang Six sigma design. 5) Reliability proof using ARSM to account the failure probability did proof six sigma quality. Start: Optimization using 5 Parameter using DX Six Sigma, then customer asked: How save is the design? by courtesy of 34

35 RDO Centrifugal Compressor Parameterization Parametric geometry definition using ANSYS BladeModeler (17 geometric parameter) Model completion and meshing using ANSYS Workbench by courtesy of 35

36 RDO Centrifugal Compressor Fluid Structure Interaction (FSI) coupling Parametric fluid simulation setup using ANSYS CFX Parametric mechanical setup using ANSYS Workbench by courtesy of 36

37 RDO Centrifugal Compressor Optimization goal: increase efficiency Constraints: 2 pressure ratio s, 66 frequency constraints, Robustness Input Parameter 21 Output Parameter 43 Constraints 68 Tolerance limit 1.34<Π T <1.36 ~13% outside Initial SA ARSM I EA I ARSM II ARSM III Total Pressure Ratio Efficiency [%] #Designs by courtesy of 37

38 RDO Centrifugal Compressor Robust Design Optimization with respect to 21 design parameters and 20 random geometry parameters, including manufacturing tolerances. Robust Design was reached after =650 design evaluations consuming. Robustness evaluation RDO optimization Sensi + first optimization step by courtesy of Robustness proof using Reliability Analysis 38

39 optislang inside ANSYS workbench What s the Difference? Ease and safe of use Minimized input, easy to use and safe to use Innovative Methodology Sensitivity analysis and optimization for large (number of variables) non-linear problems Optimization with robust defaults (ARSM, EA, GA, PARETO) Complete methodology suite to run robust design optimization Key applications Sensitivity analysis, MOP generation, Optimization Robustness evaluation and Robust Design Optimization Calibration, Model update and parameter identification contact: Johannes Will, johannes.will@dynardo.de Tel Further information: 39